Answer:
4 to the -4 power
Step-by-step explanation:
multiply the 4's and add the exponents. then divide by 4 and divide by that exponent
Answer:
3rd option
Step-by-step explanation:
( factorise numerator and denominator )
3x² - 3 ← factor out 3 from each term
= 3(x² - 1²) ← x² - 1 is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
x² - 1
= x² - 1²
= (x - 1)(x + 1) , then
3x² - 3 = 3²(x - 1)(x + 1) ← in factored form
--------------------------------
x² - 5x + 4
consider the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)
the factors are - 1 and - 4 , since
- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then
x² - 5x + 4 = (x - 1)(x - 4)
then
=
← in factored form
Answer:
1
Step-by-step explanation:
Subtract the two numbers and take the positive value ( since distance is positive)
-8/5 - (-3/5)
-8/5 + 3/5
-5/5
-1
Taking the positive value, 1
Answer:
Step-by-step explanation:
Given : A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed.
To find : A 99% confidence interval for the mean yield when the new catalyst is used ?
Solution :
Let X be the yield of the batches.
We have given, n=10 ,
, s=5.8%
Since the size of the sample is small.
We will use the student's t statistic to construct a 995 confidence interval.
![\bar X\pm t_{n-1,\frac{\alpha}{2}}\frac{s}{\sqrt n}](https://tex.z-dn.net/?f=%5Cbar%20X%5Cpm%20t_%7Bn-1%2C%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Cfrac%7Bs%7D%7B%5Csqrt%20n%7D)
From the t-table with 9 degree of freedom for ![\frac{\alpha}{2}=0.005](https://tex.z-dn.net/?f=%5Cfrac%7B%5Calpha%7D%7B2%7D%3D0.005)
![t_{n-1,\frac{\alpha}{2}}=t_{9,0.005}](https://tex.z-dn.net/?f=t_%7Bn-1%2C%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%3Dt_%7B9%2C0.005%7D)
![t_{n-1,\frac{\alpha}{2}}=3.250](https://tex.z-dn.net/?f=t_%7Bn-1%2C%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%3D3.250)
The 99% confidence interval is given by,
![CI=72.5 \pm 3.25\frac{5.8}{\sqrt{10}}](https://tex.z-dn.net/?f=CI%3D72.5%20%5Cpm%203.25%5Cfrac%7B5.8%7D%7B%5Csqrt%7B10%7D%7D)
![CI=72.5 \pm 5.96](https://tex.z-dn.net/?f=CI%3D72.5%20%5Cpm%205.96)
![CI=(72.5+5.96),(72.5-5.96)](https://tex.z-dn.net/?f=CI%3D%2872.5%2B5.96%29%2C%2872.5-5.96%29)
![CI=(66.54,78.46)](https://tex.z-dn.net/?f=CI%3D%2866.54%2C78.46%29)